Preheat the oven to 375 degrees F.
Take the buttermilk out of the refrigerator about 2 hours before preparing the batter. Line a cookie sheet with parchment paper and spray with cooking spray.
In a standing mixer, cream the butter and the sugar with the paddle attachment. Add the egg and once it is incorporated with the butter add the buttermilk. The mixture will look curdled. Add the vanilla, vinegar and food coloring.
In a medium bowl combine all of the dry ingredients together. Add the dry ingredients to the buttermilk mixture and combine completely, scraping down the sides of the bowl to get everything well mixed. Put the batter in the refrigerator for at least 1 hour.
Use a spoon or a small ice cream scoop and scoop the batter onto the cooking sheet, leaving at least a 3-inch space between scoops. Bake until the cookies are springy and firm to the touch, about 10 minutes. Allow the cookies to cool completely before filling.
Put the cream cheese and butter into the bowl of a standing mixer and using the paddle attachment, beat on medium speed until soft, about 5 minutes. Add the vanilla and lemon juice and beat to combine.
Lower the speed to slow and carefully add the sugar, 1 cup at a time. When all of the sugar has been added, switch to the whisk attachment and beat until fluffy.
Using a butter knife, spread the desired amount of frosting between 2 cookies. Arrange the completed pies on a serving dish and repeat with remaining cookies and frosting.